Nathaniel Bannister

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20242026

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math.LO2026

Condensed Sets and the Solovay Model

Nathaniel Bannister, Dianthe Basak

We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the $κ$ -pyknotic sets of Barwick--Haine and Clausen--Scholze. We then use the properti…

math.LO2025

Nonvanishing Higher Derived Limits without $w ♢_{ω_{1}}$

Nathaniel Bannister

We prove a common refinement of theorems of Bergfalk and of Casarosa and Lambie-Hanson, showing that under certain hypotheses, the higher derived limits of a certain inverse system…

math.LO2025

All you need is $A_{κ}$

Nathaniel Bannister

We show that the vanishing of higher derived limits of the system $A_{κ}$ implies the additivity of strong homology on the class of locally compact metric spaces of weight a…

math.LO2024

Locales as spaces in outer models

Nathaniel Bannister

Let M be a transitive model of set theory and X be a space in the sense of M. Is there a reasonable way to interpret X as a space in V? A general theory due to Zapletal provides a…

Condensed Sets and the Solovay Model

Nonvanishing Higher Derived Limits without w♢ω1​​

All you need is Aκ​

Locales as spaces in outer models

Nonvanishing Higher Derived Limits without $w ♢_{ω_{1}}$

All you need is $A_{κ}$